Today, Dr. Don explains the time value of money and discusses negative amortization on a home equity loan.

Time value of money

Dear Dr. Don,
Do you have a mathematical formula to calculate the time value of money? I don't know if I want a discounted lump sum or take the payments with interest. I need some way of knowing what the money is worth today vs. payments with interest. Can you help?
Tom Timevalue

Dear Tom,
The formula gets a little arcane when you're dealing with finding the present value (today's worth) of a stream of payments (annuity). The easiest way to work on this is to use Bloomberg.com's mortgage calculator. There are four variables: the interest rate, the payment amount, the number of years and the loan amount -- which is the present value. You have to provide the interest rate and the number of years the payments will take place. Then either enter the present value or the monthly payment, and the calculator will solve for the other variable. Alternately, most spreadsheet packages have formulas to solve for payment, present value or the interest rate. You can use the spreadsheet's help feature to walk you through inputting the information.

If you're trying to decide whether to buy an annuity, don't forget to consider the tax implications of your actions. Don't just rely on your investment professional; consult with a tax planner too.

Negative amortization

Dear Dr. Don,
How often does the variable rate on a home equity loan adjust? When it does adjust, how does the change affect the monthly payment or the total balance? In September 1999 I took out a home equity loan of \$43,019 at a variable rate of 8.78 for 20 years. Since then my monthly payment has never increased but my loan balance has increased six times. When I asked my lender for the payoff balance and I was told it was \$43,645. How can that be true?
Vexing Variable

Dear Vex,
You're experiencing negative amortization. When your payment is capped, then the difference between your payment and what the uncapped payment would be is added to the loan balance. This happens when your variable interest rate is reset to a higher rate. The capped payment no longer covers the interest expense. The unpaid interest expense is added to your loan balance. If your home equity loan had an introductory rate, the first interest rate reset is virtually certain to be higher than the initial rate, resulting in negative amortization.

Your loan documents spell out how often the interest rate is adjusted, the index and the spread to the index. The typical home equity loan is priced off the prime rate. Since the prime rate usually increases when the Federal Reserve raises the Fed Funds rate, the interest rate on these loans are going higher. Most variable rate home equity loans have a spread up to 1 percentage point over the prime rate. You can follow the prime rate and other variable rate indexes on this site's Watch Market Rates page.

A variable rate loan can have both interest rate caps and payment caps. Payment caps limit the increase in the mortgage payment. Your loan may well have an initial 12-month payment cap. Payment caps are helpful in budgeting. You'll know for certain what your payment will be during the first 12 months, but if the interest rate goes higher you'll experience negative amortization. Interest rate caps limit the increase in the variable rate. There are periodic caps and lifetime caps. A periodic cap limits the interest rate increase for one reset period while a lifetime cap spells out the highest interest rate you can be charged on the loan.

Can you be in a situation where your loan balance is increasing? Yes, you can. Since your loan is so recent, make sure you won't incur any prepayment penalties if you decide to pay off the loan.

 Related information: Dr. Don's biography Submit a question to Dr. Don Archive of Dr. Don columns

-- Posted: June 21, 2000

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